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In a dissent she summarised in court, Justice Sonia Sotomayor said, "History will not look kindly on the court's misguided decision today, nor should it".

Justice Sotomayor wrote that based on the evidence in the case "a reasonable observer would conclude that the proclamation was motivated by anti-Muslim animus".

She said her colleagues in the majority arrived at the opposite result by "ignoring the facts, misconstruing our legal precedent and turning a blind eye to the pain and suffering the proclamation inflicts upon countless families and individuals, many of whom are United States citizens".

The 5-4 decision today is the court's first substantive ruling on a Trump administration policy, and the president quickly tweeted his reaction: "Wow!" Picture: AP (AP)

The policy applies to travellers from five countries with overwhelmingly Muslim populations – Iran, Libya, Somalia, Syria and Yemen.

It also affects two non-Muslim countries, blocking travellers from North Korea and some Venezuelan government officials and their families.

A sixth majority Muslim country, Chad, was removed from the list in April after improving "its identity-management and information sharing practices", Mr Trump said in a proclamation.

The administration had pointed to the Chad decision to show that the restrictions are premised only on national security concerns.

The travel ban has been fully in place since December, when the justices put the brakes on lower court rulings that had ruled the policy out of bounds and blocked part of it from being enforced. Picture: AP (AP)

The challengers however argued that the court could not just ignore all that has happened, beginning with Mr Trump's campaign tweets to prevent the entry of Muslims into the United States.

The travel ban has long been central to Mr Trump's presidency.

He proposed a broad, all-encompassing Muslim ban during the presidential campaign in 2015, drawing swift rebukes from Republicans as well as Democrats.

And within a week of taking office, the first travel ban was announced with little notice, sparking chaos at airports and protests across the nation.

While the ban has changed shape since then, it has remained a key part of Mr Trump's "America First" vision, with the president believing that the restriction, taken in tandem with his promised wall at the southern border, would make the Unites States safer from potentially hostile foreigners.

Justice Sotomayor wrote that based on the evidence in the case "a reasonable observer would conclude that the proclamation was motivated by anti-Muslim animus". Picture: CrowdSpark (CrowdSpark)

The current version dates from last September and it followed what the administration has called a thorough review by several federal agencies, although no such review has been shared with courts or the public.

Federal trial judges in Hawaii and Maryland had blocked the travel ban from taking effect, finding that the new version looked too much like its predecessors.

Those rulings that were largely upheld by federal appeals courts in Richmond, Virginia, and San Francisco.

But the Supreme Court came to a different conclusion today. The policy has "a legitimate grounding in national security concerns", and it has several moderating features, including a waiver program that would allow some people from the affected countries to enter the US, Chief Justice Roberts said.

The administration has said that 809 people have received waivers since the ban took full effect in December.

Chief Justice Roberts he was careful not to endorse either Mr Trump's provocative statements about immigration in general or Muslims in particular. Picture: AP (AP)

Chief Justice Roberts wrote that presidents have frequently used their power to talk to the nation "to espouse the principles of religious freedom and tolerance on which this nation was founded".

But he added that presidents and the country have not always lived up "to those inspiring words".